1.1 Field of the Invention
This invention relates generally to a method and system for characterizing subsurface electromagnetic (EM) measurements to determine wellbore and formation properties and, more particularly, to a technique for obtaining the caliper of a wellbore and the electric and geometric properties of the surrounding rock formations from subsurface EM measurements. The invention has general application in the well logging art, but is particularly useful in measuring-while-drilling.
1.2 Description of Related Art
In order to improve oil and gas drilling operations, it is necessary to gather as much information as possible on the properties of the subsurface earth formation where deposits are believed to exist. Such properties include the resistivity of the earth formations traversed by the well borehole, in addition to data on the properties and configuration of the borehole itself.
The collection of downhole information, also referred to as logging, is realized in different ways. A well tool, comprising transmitting and sensing devices for measuring various properties, can be lowered into the borehole on the end of a cable, or wireline. With this type of wireline logging, borehole and formation parameters are measured as a function of depth, i.e., while the tool is being pulled uphole. An alternative to wireline logging techniques is the collection of data on downhole conditions during the drilling process. By collecting and processing such information during the drilling process, the driller can modify or correct key steps of the operation to optimize performance. While-drilling measurements are also less affected by significant hole washout and invasion, which typically occur at the wireline stage.
Schemes for collecting data of downhole conditions and movement of the drilling assembly during the drilling operation are known as measurement-while-drilling (MWD) techniques. Similar techniques focusing more on measurement of formation parameters than on movement of the drilling assembly are know as logging-while-drilling (LWD). However, the terms MWD and LWD are often used interchangeably, and the use of either term herein should be understood to include both the collection of formation and borehole information, as well as data on movement of the drilling assembly.
The processes often employed to measure the subsurface characteristics are subject to significant errors unless information on the borehole size, the borehole configuration, and the electric and geometric properties of the invaded zone are also taken into account. During the drilling process, mud filtrate penetrates into the virgin formation, creating an invaded zone. Knowledge of the borehole diameter, also known as the caliper, is essential to correct measurements that are sensitive to standoff. Monitoring the hole size can also be critical for the successful drilling and completion of a well when hole stability is of concern.
There is a lack of a reliable fullbore caliper measurement while drilling. Wireline caliper measurements may not be an option when critical decisions need to be made while drilling. Furthermore, hole conditions will likely have changed by the time a wireline caliper is run. In highly deviated and horizontal wells, both standoff (distance between the tool and borehole wall) and invasion are azimuthally varying. Interpreting measurement logs that are sensitive to standoff may require the knowledge of standoff at different directions. Thus, a fullbore caliper is extremely useful for interpreting azimuthal measurements.
U.S. Pat. No. 4,407,157 describes a technique for measuring a borehole caliper by incorporating a mechanical apparatus with extending contact arms that are forced against the sidewall of the borehole. Such mechanical apparatus have practical limitations and are limited in the range of diameter measurement they provide. Due to the unsuitability of mechanical calipers to drilling operations, indirect techniques of determining borehole calipers have been proposed.
Conventional caliper measurement techniques include acoustic transducers that transmit ultrasonic signals to the borehole wall. U.S. Pat. No. 5,469,736 describes an apparatus for measuring the caliper of a borehole by transmitting ultrasonic signals during a drilling operation. U.S. Pat. No. 5,397,893 describes a method for analyzing formation data from a MWD tool incorporating an acoustic caliper. U.S. Pat. No. 5,886,303 describes a logging tool including an acoustic transmitter for obtaining the borehole caliper while drilling. However, the techniques proposed with acoustic calipers entail measurements employing standoff and travel time calculations, resulting in data of limited accuracy. Sound wave reflections in soft formations may also be too weak to be accurately detected, leading to loss of signals.
U.S. Pat. No. 4,791,797 proposes another technique for measuring a borehole caliper while drilling. The ""797 patent describes a process whereby two tools having different sensitivities are used to take downhole measurements. The obtained measurements are then combined in an iterative process to determine the borehole readings. In addition to requiring combined multiple computations and iterations, the techniques proposed by the ""797 patent also require independent lithology identification.
Downhole measurements are also affected by mud filtrate invasion that changes the properties of the rock near the wellbore. The traditional approach in invasion analysis, based on plotted curves known as xe2x80x9ctornado charts,xe2x80x9d requires the input data to be corrected for the effects of the borehole on the measurements. This is typically done, most of the time unjustified, assuming the hole size to be the same as the bit size of the drilling tool, since the actual hole size is rarely measured while drilling. Moreover, with more than three subsurface measurements, reading from the tornado charts produces results that depend on which three resistivities are taken as inputs.
The wealth of information provided by conventional multisensor and LWD tools makes these tools ideal for accurate borehole and formation definition through inversion to improve oil, gas, and water exploration. Inversion algorithms typically implement a forward modeling capability that can predict the well tool response for a given formation. See Lin, Y. et al., Inversion of induction logging data using the least square technique, SPWLA Twenty-Fifth Annual Logging Symposium, 1984; Mezzaesta, A. et al., Integrated 2-D interpretation of resistivity logging measurement by inversion methods, SPWLA Thirty-Sixth Annual Logging Symposium, 1995. However, accurate characterization of the tool response usually requires sophisticated and computer intensive numerical forward modeling codes to solve the fundamental equations governing the electromagnetic energy distribution of the measurements. The speed of current two-dimensional (2D) inversion programs is a major limitation preventing their universal application.
On the other hand, a physical concept that describes laterolog-type well tool responses to invasion has been used for many years. This is the pseudo-geometrical factor J, which is defined by the relation
Ra=J Rxo+(1xe2x88x92J)Rt,xe2x80x83xe2x80x83(1)
where Ra is the apparent formation resistivity of the measurement, Rxo is the invaded zone resistivity, and Rt is the actual resistivity of the virgin formation.
The pseudo-geometrical factor J is simply interpreted as the percentage of the measured signal coming from the invaded zone in the absence of a borehole. Obviously, J should depend on the invasion diameter Di. Another deficiency of the pseudo-geometrical factor is that it not only depends on the invasion diameter but also on the contrast between Rt and Rxo. This limits its utility for practical calculations since one has to tabulate all the values of J under different contrast and for different invasion diameters.
It is desirable to have a simplified method and system for characterizing the response of a subsurface EM measurement to accurately determine the fullbore electric caliper as well as the electric and geometric properties of the invaded zone and the virgin formation. It is also desirable to implement a fast inversion technique that can accurately reproduce the response of a well tool to borehole and formation parameters.
One aspect of the invention is a method for characterizing the response of a subsurface resistivity measurement to determine a characteristic of a borehole within the subsurface and/or a characteristic of a formation surrounding the borehole. The method includes obtaining subsurface resistivity measurement data with a well tool disposed within the borehole; and fitting the obtained resistivity measurement data to an electric circuit model to determine the borehole characteristic and/or the formation characteristic, the circuit model being representative of a response of the well tool to borehole and formation parameters, the model including at least one resistor-in-parallel component.
Another aspect of the invention is a method for determining a characteristic of a borehole traversing an earth formation and/or a characteristic of the formation surrounding the borehole using measurement data obtained from a well tool disposed within the borehole. The method includes reproducing a response of the well tool to borehole and formation parameters using an electric circuit model, the model being characterized by at least one resistor-in-parallel component; and fitting the obtained measurement data to the reproduced response to determine the borehole characteristic and/or the formation characteristic.
Another aspect of the invention is a system for characterizing the response of a subsurface resistivity measurement to determine a characteristic of a borehole within the subsurface and/or a characteristic of a formation surrounding the borehole, the system including a well tool and an apparatus adapted to be coupled to the well tool, the tool being adapted to transmit and receive electromagnetic energy when disposed in the borehole, the apparatus being adapted to respond to measurement data generated by the tool and associated with the electromagnetic energy. The apparatus includes means for receiving the measurement data; means for storing model parameters representative of a response of the well tool to borehole and formation properties, the model being characterized by an electric circuit having at least one resistor-in-parallel component; and means for comparing the received measurement data to the stored model parameters to determine the borehole characteristic and/or the formation characteristic.
Another aspect of the invention is a system for determining a characteristic of a borehole traversing an earth formation and/or a characteristic of the formation surrounding the borehole, the system including a well tool and an apparatus adapted to be coupled to the well tool, the tool being adapted to transmit and receive electromagnetic energy through the borehole and the formation when disposed in the borehole, the apparatus being adapted to respond to measurement data generated by the tool and associated with the electromagnetic energy. The apparatus includes means for receiving the measurement data; means for storing model parameters representative of a response of the well tool to borehole and formation properties, the model being characterized by an electric circuit having at least one resistor-in-parallel component; and means for comparing the received measurement data to the stored model parameters to determine the borehole characteristic and/or the formation characteristic.